Thread Subject:

interpolation

hi my problem is this
i know the value of an unknown funtion in 8 points on the
circumference of the circle
i need to know the value of the funtion in some 20 ppoints on the
circunference of the circle+the value of function at the centre of the
circle and its values along various lines joining the centre and
circunference of the circle
i am a beginner to matlab so iwould really be obliged to you if you
can send me a detailed answer with code if possible
bye
sundar

First, if you know the value of the function at 8 points on the
circumference of the circle, you can use interpolation by mapping the
circumference into a function of 1 variable, the polar angle theta.
Define 9 points theta_1, theta_2, theta_3 ... theta_8, theta_9
where theta_9 = theta_1 + 2*pi
Then interpolate (you choose the degree of the interpolating polynomial
... cubic?) to the polar angles of interest and transform back again.

The second part of your question concerns values of the function at
interior points. This is an ill-posed question. Knowing the value of a
function at a boundary isn't enough information to determine the
function away from the boundary. Think of the one-dimensional
analog ... given the value of a function at 2 points, all you can do
is draw a straight line between them (linear interpolation). But
there is no reason to have any faith in that procedure.

However, if that's what you have in mind, here is a suggestion.
Interpolate the values of the function at the 8 points onto a set of
equally spaced polar angles (these could be your 20 points). Then take
the mean of the function values at these points as the value at the
center of the circle. Now do linear interpolation from points on the
circumference to the center. Of course, your interpolated function
will have a discontinuous derivative at the center.

>hi my problem is this
>i know the value of an unknown funtion in 8 points on the
>circumference of the circle
>i need to know the value of the funtion in some 20 ppoints on the
>circunference of the circle+the value of function at the centre of the
>circle and its values along various lines joining the centre and
>circunference of the circle
>i am a beginner to matlab so iwould really be obliged to you if you
>can send me a detailed answer with code if possible

> hi my problem is this
> i know the value of an unknown funtion in 8 points on the
> circumference of the circle
> i need to know the value of the funtion in some 20 ppoints on the
> circunference of the circle+the value of function at the centre of the
> circle and its values along various lines joining the centre and
> circunference of the circle
> i am a beginner to matlab so iwould really be obliged to you if you
> can send me a detailed answer with code if possible
> bye
> sundar

>hi my problem is this
>i know the value of an unknown funtion in 8 points on the
>circumference of the circle
>i need to know the value of the funtion in some 20 ppoints on the
>circunference of the circle+the value of function at the centre of the
>circle and its values along various lines joining the centre and
>circunference of the circle
>i am a beginner to matlab so iwould really be obliged to you if you
>can send me a detailed answer with code if possible